Quadrupole Ordering and Rattling Motion of Clathrate Compound Pr3Pd20Ge6

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We have investigated the quadrupole ordering of 4f-electrons and the rattling motion of guest rare-earth ions in the clathrate compound Pr3Pd20Ge6 using ultrasonic measurements. The elastic constants (C_{11} - C_{12})/2 and C_{44} exhibit considerable softening at low temperatures. A minimum of (C_{11} - C_{12})/2 at T_{\text{Q1}} = 0.25 K indicates antiferroquadrupole ordering associated with a \Gamma_{3} doublet of a crystal-field ground state at the 8c site, while a minimum of C_{44} at T_{\text{Q2}} = 60 mK indicates the ferroquadrupole ordering of a \Gamma_{5} triplet of a crystal-field ground state at the 4a site. The antiferroquadrupole phase depending on magnetic field direction shows a highly anisotropic behavior. The field-induced ordered phase due to the level crossing of the CEF ground state at the 8c site in magnetic fields along the [001] direction has been found. Furthermore, for the elastic constant C_{44} and the attenuation coefficient \alpha_{44} we found a frequency dependence at two different temperatures of 15 and 25 K, which we describe in terms of the Debye-type dispersion with an Arrhenius-type relaxation time \tau = \tau_{0}\exp(E/k_{\text{B}} T) for two different activation energies of E_{\text{L}} = 102 K and E_{\text{H}} = 198 K. These ultrasonic dispersions are caused by the thermally activated rattling motions of guest rare-earth Pr3+ ions at the 4a site of Pr3Pd20Ge6.
2012-03-15